wo blocks of ice, one four times as heavy as the other, are at rest on a frozen ike. A person pushes each block the same distance \( d \). Ignore friction and ssume that an equal force \( \vec{F} \) is oxerted on each block. Part A Part B Compared to the speed of the heavier block, what is the speed of the light block after both blocks move the same distance d? View Available Hint(s) one quarter as fast half as fast the same speed twice as fast four times as fast

When the person applies the same force \( \vec{F} \) to both blocks, according to Newton's second law \( F = ma \), the acceleration \( a \) of an object is inversely proportional to its mass. The lighter block (let's say mass \( m \)) will accelerate more than the heavier block (mass \( 4m \)). Thus, while both blocks cover the same distance \( d \), the lighter block will achieve a higher speed. Now, using the relationship derived from kinematics, the speed of an object can be determined by \( v^2 = u^2 + 2ad \). Since both blocks start from rest (initial speed \( u = 0 \)), their final speeds depend solely on their respective accelerations over the same distance \( d \). Given that the lighter block has greater acceleration, it achieves a speed that is indeed higher than that of the heavier block. Specifically, the speeds will have a ratio based on their masses, leading us to the conclusion that the lighter block will be moving **twice as fast** as the heavier block once they both have traveled the same distance \( d \).